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Write (a) the contrapositive and (b) the inverse of the following statement.

If Abby is not here, then she is not well.

Short Answer

Expert verified

a. The contrapositive of 鈥淚f Abby is not here, then she is not well鈥 is鈥淚f she is well then Abby is here鈥.

b. The inverse of 鈥淚f Abby is not here, then she is not well鈥 is鈥淚f Abby is here then she is well鈥.

Step by step solution

01

a.Step 1. Apply the concept of the contrapositive statement.

A contrapositive of any statement is the switching of hypothesis and the conclusion of the inverse of that statement such thatto form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.

02

Step 2. Write the inverse of the statement.

Consider the statement 鈥淚f Abby is not here, then she is not well鈥.

Write the inverse of the conditional statement as follows:

If Abby is here, then she is well.

03

Step 3. Write the contrapositive of the statement.

Interchange the hypothesis and the conclusion of the inverse statement to write the contrapositive of the statement as follows:

If she is well then Abby is here.

Therefore, the contrapositive of the statement is 鈥淚f she is well then Abby is here鈥.

04

b.Step 1- Apply the concept of the inverse of a statement.

To form the inverse of a conditional statement, take the negation of both the hypothesis and the conclusion.

05

Step 2. Write the inverse of the statement.

Consider the statement鈥淚f Abby is not here, then she is not well鈥.

Take the negation of the hypothesis and the conclusion to write the inverse of the statement.

06

Step 3. Step description.

The negation of the hypothesis and the conclusion is 鈥淚f Abby is here, then she is well.鈥.

Therefore, the inverse of the statement is 鈥淚f Abby is here, then she is well.鈥.

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